Efficient, high-resolution topology optimization method based on convolutional neural networks

Frontiers of Mechanical Engineering - Tập 16 Số 1 - Trang 80-96 - 2021
Xue Liu1, Jie Liu1, Guilin Wen1, Hongxin Wang1
1State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha 410082, China

Tóm tắt

AbstractTopology optimization is a pioneer design method that can provide various candidates with high mechanical properties. However, high resolution is desired for optimum structures, but it normally leads to a computationally intractable puzzle, especially for the solid isotropic material with penalization (SIMP) method. In this study, an efficient, high-resolution topology optimization method is developed based on the superresolution convolutional neural network (SRCNN) technique in the framework of SIMP. SRCNN involves four processes, namely, refinement, path extraction and representation, nonlinear mapping, and image reconstruction. High computational efficiency is achieved with a pooling strategy that can balance the number of finite element analyses and the output mesh in the optimization process. A combined treatment method that uses 2D SRCNN is built as another speed-up strategy to reduce the high computational cost and memory requirements for 3D topology optimization problems. Typical examples show that the high-resolution topology optimization method using SRCNN demonstrates excellent applicability and high efficiency when used for 2D and 3D problems with arbitrary boundary conditions, any design domain shape, and varied load.

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Tài liệu tham khảo

Bendsøe M P, Kikuchi N. Generating optimal topologies in structural design using a homogenization method. Computer Methods in Applied Mechanics and Engineering, 1988, 71(2): 197–224

Bendsøe M P. Optimal shape design as a material distribution problem. Structural Optimization, 1989, 1(4): 193–202

Sigmund O A. 99 line topology optimization code written in Matlab. Structural and Multidisciplinary Optimization, 2001, 21(2): 120–127

Rozvany G I N, Zhou M, Birker T. Generalized shape optimization without homogenization. Structural Optimization, 1992, 4(3–4): 250–252

Xie Y M, Steven G P. A simple evolutionary procedure for structural optimization. Computers & Structures, 1993, 49(5): 885–896

Querin O M, Steven G P, Xie Y M. Evolutionary structural optimisation (ESO) using a bidirectional algorithm. Engineering Computations, 1998, 15(8): 1031–1048

Huang X, Xie Y M. Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite Elements in Analysis and Design, 2007, 43(14): 1039–1049

Rozvany G I N. A critical review of established methods of structural topology optimization. Structural and Multidisciplinary Optimization, 2009, 37(3): 217–237

Xia L, Zhang L, Xia Q, et al. Stress-based topology optimization using bi-directional evolutionary structural optimization method. Computer Methods in Applied Mechanics and Engineering, 2018, 333: 356–370

Wang M Y, Wang X, Guo D. A level set method for structural topology optimization. Computer Methods in Applied Mechanics and Engineering, 2003, 192(1–2): 227–246

Wei P, Li Z, Li X, et al. An 88-line MATLAB code for the parameterized level set method based topology optimization using radial basis functions. Structural and Multidisciplinary Optimization, 2018, 58(2): 831–849

Xia Q, Shi T, Xia L. Stable hole nucleation in level set based topology optimization by using the material removal scheme of BESO. Computer Methods in Applied Mechanics and Engineering, 2019, 343: 438–452

Xia Q, Shi T. Generalized hole nucleation through BESO for the level set based topology optimization of multi-material structures. Computer Methods in Applied Mechanics and Engineering, 2019, 355: 216–233

Liu H, Zong H, Shi T, et al. M-VCUT level set method for optimizing cellular structures. Computer Methods in Applied Mechanics and Engineering, 2020, 367: 113154

Guo X, Zhang W, Zhong W. Doing topology optimization explicitly and geometrically—A new moving morphable components based framework. Journal of Applied Mechanics, 2014, 81(8): 081009

Zhang W, Chen J, Zhu X, et al. Explicit three dimensional topology optimization via moving morphable void (MMV) approach. Computer Methods in Applied Mechanics and Engineering, 2017, 322: 590–614

Lei X, Liu C, Du Z, et al. Machine learning-driven real-time topology optimization under moving morphable component-based framework. Journal of Applied Mechanics, 2019, 86(1): 011004

Cai S, Zhang W. An adaptive bubble method for structural shape and topology optimization. Computer Methods in Applied Mechanics and Engineering, 2020, 360: 112778

Zhu J H, Zhang W H, Xia L. Topology optimization in aircraft and aerospace structures design. Archives of Computational Methods in Engineering, 2016, 23(4): 595–622

Fu Y F, Rolfe B, Chiu L N S, et al. Design and experimental validation of self-supporting topologies for additive manufacturing. Virtual and Physical Prototyping, 2019, 14(4): 382–394

Meng L, Zhang W, Quan D, et al. From topology optimization design to additive manufacturing: Today’s success and tomorrow’s roadmap. Archives of Computational Methods in Engineering, 2020, 27(3): 805–830

Chin T W, Kennedy G J. Large-scale compliance-minimization and buckling topology optimization of the undeformed common research model wing. In: Proceedings of the 57th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference. San Diego: AIAA, 2016

Liu J, Ou H, He J, et al. Topological design of a lightweight sandwich aircraft spoiler. Materials, 2019, 12(19): 3225

Sutradhar A, Park J, Carrau D, et al. Designing patient-specific 3D printed craniofacial implants using a novel topology optimization method. Medical & Biological Engineering & Computing, 2016, 54(7): 1123–1135

Alexandersen J, Sigmund O, Aage N. Large scale three-dimensional topology optimisation of heat sinks cooled by natural convection. International Journal of Heat and Mass Transfer, 2016, 100: 876–891

Ye M, Gao L, Li H. A design framework for gradually stiffer mechanical metamaterial induced by negative Poisson’s ratio property. Materials & Design, 2020, 192: 108751

Groen J P, Sigmund O. Homogenization-based topology optimization for high-resolution manufacturable microstructures. International Journal for Numerical Methods in Engineering, 2018, 113(8): 1148–1163

Wu Z, Xia L, Wang S, et al. Topology optimization of hierarchical lattice structures with substructuring. Computer Methods in Applied Mechanics and Engineering, 2019, 345: 602–617

Zhu B, Skouras M, Chen D, et al. Two-scale topology optimization with microstructures. ACM Transactions on Graphics, 2017, 36(4): 120b

Wang Y, Xu H, Pasini D. Multiscale isogeometric topology optimization for lattice materials. Computer Methods in Applied Mechanics and Engineering, 2017, 316: 568–585

Li H, Luo Z, Gao L, et al. Topology optimization for concurrent design of structures with multi-patch microstructures by level sets. Computer Methods in Applied Mechanics and Engineering, 2018, 331: 536–561

Li H, Luo Z, Xiao M, et al. A new multiscale topology optimization method for multiphase composite structures of frequency response with level sets. Computer Methods in Applied Mechanics and Engineering, 2019, 356: 116–144

Christiansen A N, Bærentzen J A, Nobel-Jørgensen M, et al. Combined shape and topology optimization of 3D structures. Computers & Graphics, 2015, 46: 25–35

Wang H, Liu J, Wen G. An efficient evolutionary structural optimization method with smooth edges based on the game of building blocks. Engineering Optimization, 2019, 51(12): 2089–2018

Nguyen T H, Paulino G H, Song J, et al. A computational paradigm for multiresolution topology optimization (MTOP). Structural and Multidisciplinary Optimization, 2010, 41(4): 525–539

Nguyen-Xuan H. A polytree-based adaptive polygonal finite element method for topology optimization. International Journal for Numerical Methods in Engineering, 2017, 110(10): 972–1000

Leader M K, Chin T W, Kennedy G J. High-resolution topology optimization with stress and natural frequency constraints. AIAA Journal, 2019, 57(8): 3562–3578

Chin T W, Leader M K, Kennedy G J. A scalable framework for large-scale 3D multimaterial topology optimization with octree-based mesh adaptation. Advances in Engineering Software, 2019, 135: 102682

Groen J P, Langelaar M, Sigmund O, et al. Higher-order multiresolution topology optimization using the finite cell method. International Journal for Numerical Methods in Engineering, 2017, 110(10): 903–920

Gupta D K, van Keulen F, Langelaar M. Design and analysis adaptivity in multi-resolution topology optimization. 2018, arXiv:1811.09821v1

Xiao M, Lu D, Breitkopf P, et al. Multi-grid reduced-order topology optimization. Structural and Multidisciplinary Optimization, 2020, 61: 2319–2341

Lieu Q X, Lee J. Multiresolution topology optimization using isogeometric analysis. International Journal for Numerical Methods in Engineering, 2017, 112(13): 2025–2047

Xu M, Xia L, Wang S, et al. An isogeometric approach to topology optimization of spatially graded hierarchical structures. Composite Structures, 2019, 225: 111171

Wang Y, Liao Z, Ye M, et al. An efficient isogeometric topology optimization using multilevel mesh, MGCG and local-update strategy. Advances in Engineering Software, 2020, 139: 102733

Wang H, Liu J, Wen G. Achieving large-scale or high-resolution topology optimization based on modified BESO and XEFM. 2019, arXiv:1908.07157

Kim Y Y, Yoon G H. Multi-resolution multi-scale topology optimization—A new paradigm. International Journal of Solids and Structures, 2000, 37(39): 5529–5559

Stainko R. An adaptive multilevel approach to the minimal compliance problem in topology optimization. Communications in Numerical Methods in Engineering, 2006, 22(2): 109–118

Liao Z, Zhang Y, Wang Y, et al. A triple acceleration method for topology optimization. Structural and Multidisciplinary Optimization, 2019, 60(2): 727–744

Suresh K. Generating 3D topologies with multiple constraints on the GPU. In: Proceedings of the 10th World Congress on Structural and Multidisciplinary Optimization. Orlando, 2013, 1–9

Challis V J, Roberts A P, Grotowski J F. High resolution topology optimization using graphics processing units (GPUs). Structural and Multidisciplinary Optimization, 2014, 49(2): 315–325

Aage N, Andreassen E, Lazarov B S, et al. Giga-voxel computational morphogenesis for structural design. Nature, 2017, 550 (7674): 84–86

Long K, Gu C, Wang X, et al. A novel minimum weight formulation of topology optimization implemented with reanalysis approach. International Journal for Numerical Methods in Engineering, 2019, 120(5): 567–579

Wang Y, Liao Z, Shi S, et al. Data-driven structural design optimization for petal-shaped auxetics using isogeometric analysis. Computer Modeling in Engineering & Sciences, 2020, 122(2): 433–458

Zhou Y, Zhan H, Zhang W, et al. A new data-driven topology optimization framework for structural optimization. Computers & Structures, 2020, 239: 106310

Sosnovik I, Oseledets I. Neural networks for topology optimization. Russian Journal of Numerical Analysis and Mathematical Modelling, 2019, 34(4): 215–223

Banga S, Gehani H, Bhilare S, et al. 3D topology optimization using convolutional neural networks. 2018, arXiv:1808.07440v1

Zhang Y, Chen A, Peng B, et al. A deep convolutional neural network for topology optimization with strong generalization ability. 2019, arXiv:1901.07761v1

Li B, Huang C, Li X, et al. Non-iterative structural topology optimization using deep learning. Computer-Aided Design, 2019, 115: 172–180

Dong C, Loy C C, He K, et al. Image super-resolution using deep convolutional networks. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2016, 38(2): 295–307

Bendsøe M P, Sigmund O. Topology Optimization: Theory, Methods, and Applications. Berlin: Springer, 2013, 37–40

Andreassen E, Clausen A, Schevenels M, et al. Efficient topology optimization in MATLAB using 88 lines of code. Structural and Multidisciplinary Optimization, 2011, 43(1): 1–16

Liu H, Wang Y, Zong H, et al. Efficient structure topology optimization by using the multiscale finite element method. Structural and Multidisciplinary Optimization, 2018, 58(4): 1411–1430

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Frontiers of Mechanical Engineering

Tập 16 Số 1

80-96

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